Limit cycles and integrability in a class of system with a high-order critical point

作者：Feng Li^*

来源：Nonlinear Dynamics, 2013, 73(1-2): 665-670.

DOI：10.1007/s11071-013-0820-0

• High-order critical point
• Nilpotent critical point
• Center
• Focus
• Bifurcation of limit cycle

In this paper, a class of polynomial differential system with high-order critical point are investigated. The system could be changed into a system with a 3-order nilpotent critical point. Finally, an example was given, with the help of computer algebra system MATHEMATICA, the first three quasi-Lyapunov constants are deduced. As a result, sufficient and necessary conditions in order to have a center are obtained. The fact that there three small amplitude limit cycles created from the 3-order nilpotent critical point is also proved.

• 出版日期2013-7